TOC regular language

Question

Is regular languages closed under

1)Infinite Union

2)Infinite Intersection

Answer 1

Not closed in both cases

Eg :{£} ,{a} {aa} {aaa}  {aaa}........ = a* (regular )

     : {null } {ab} {aabb} {aaabbb}......= a^nb^n (cfl )

So infinite union of regular may be regular or cfl !! Therefore it is not closed under infinite union .

Same case occurs with infinite intersection also so it is also not closed under infinite intersection this can be proved by property of  boolean algebra.